Patsy has cheerleading practice every fourth day. She wants to be in the school play, but they have practice every sixth day. If both start on September 5th, what would be the next date she has to choose between cheerleading and play practice? Show your work and explain.

the LCM (lowest common multiple) of 4 and 6 is 12

on September 17th she will have to choose between
... the 4th cheerleading practice and the 3rd play practice

I agree

To determine the next date when Patsy has to choose between cheerleading and play practice, we need to find the least common multiple (LCM) of 4 and 6, which will give us the interval between these choices.

Let's break it down step by step:

1. First, let's list out the multiples of each number until we find a common multiple:
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, ...
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, ...

2. By examining the multiples, we can see that 12 is the smallest common multiple of 4 and 6.

3. Since Patsy started both cheerleading and play practice on September 5th, we need to find the next date that is divisible by 12.

4. Counting the number of days from September 5th, we find that the next date that is divisible by 12 is September 17th.

Therefore, the next date Patsy has to choose between cheerleading and play practice would be September 17th.